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Proof step 38 from proof okarray-put-07 (previous step)

okarray(val, ty, i, st) ⊦ is_referencevalue(val) ∧ val .refval -- _type ∈ st[r -- sk, val0] ∧ is_typevalue(st[r -- sk, val0][val .refval -- _type]) ∧ is_arraytype((st[r -- sk, val0][val .refval -- _type]) .type) ∧ (st[r -- sk, val0][val .refval -- _type]) .type .type ≤ ty ∧ val .refval ≠ jvmref ∧ val .refval -- _length ∈ st[r -- sk, val0] ∧ (st[r -- sk, val0][val .refval -- _length]) = intval(i) ∧ 0 ≤ i ∧ is_arrayref(val .refval, i, st[r -- sk, val0]) ∧ (∀ j. ¬ j < 0 ∧ ¬ i ≤ j → okval(st[r -- sk, val0][val .refval -- j '], ty)), refval(r) = val

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
⊦ ¬ is_referencevalue(val) → ¬ okarray(val, ty, i, st)
Proof step 21:
⊦ val .refval = jvmref → ¬ okarray(val, ty, i, st)
Proof step 37:
okarray(val, ty, i, st), is_referencevalue(val) ⊦ refval(r) = val, val .refval = jvmref, (0 ≤ j ∧ j < i → okval(st[r -- sk, val0][val .refval -- j '], ty)) ∧ is_arrayref(val .refval, i, st[r -- sk, val0]) ∧ ¬ i < 0 ∧ (st[r -- sk, val0][val .refval -- _length]) = intval(i) ∧ (val .refval = r ∧ _length = sk ∨ val .refval -- _length ∈ st) ∧ (st[r -- sk, val0][val .refval -- _type]) .type .type ≤ ty ∧ is_arraytype((st[r -- sk, val0][val .refval -- _type]) .type) ∧ is_typevalue(st[r -- sk, val0][val .refval -- _type]) ∧ (val .refval = r ∧ _type = sk ∨ val .refval -- _type ∈ st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st])]]